An ideal gas is expanded adiabatically from (p 1 , V 1 ) to (p 2 , V 2 ). Then it is compressed isobarically to (p 2 , V 1 ). Finally the pressure is increased to p 1 at constant volume V 1 . Show that the efficiency of the cycle is
η = 1 – γ (V 2 /V 1 – 1)/(p 1 /p 2 – 1),
Where γ = C p /C v .
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. The cycle is shown in the Fig.
The work the system does in the cycle is
W = 
= 
+ p 2 (V 1 – V 2 ).
Because AB is adiabatic and an ideal gas has the equations pV = nkT and C p = C v + R, we get
= – 
= – C v (T 2 – T 1 )
= 
(p 2 V 2 – p 1 V 1 )
During the CA part of the cycle the gas absorbs heat
Q = 
= 
= C v (T 1 – T 2 )
= 
V 1 (p 2 – p 1 ).
Hence, the efficiency of the engine is
η = 
= 1 – γ 
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